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          <h1 class="post-title" itemprop="name headline">第十届全国大学生数学竞赛LaTeX模板</h1>
        

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        <p><strong>第十届全国大学生数学竞赛LaTeX模板</strong></p>
<p>过去一周的数学竞赛已经告一段落，在考前的几次模拟赛题中，八一都是以这个模板给同学们进行试题命题，想必大家看到之后，都很想去学习一番LaTeX技巧，这里我就把自己的源码贴到下面供大家练习，也预祝各位好朋友相聚哈尔滨！本文档的pdf以及tex源码，请点以下链接进行即可下载。</p>
<a id="more"></a>
<p>本文档pdf：<a href="CMC.pdf">CMC文档</a>               </p>
<p>本文档tex：<a href="CMC.tex">CMC源码</a></p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span 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class="line">182</span><br><span class="line">183</span><br><span class="line">184</span><br><span class="line">185</span><br><span class="line">186</span><br><span class="line">187</span><br><span class="line">188</span><br><span class="line">189</span><br><span class="line">190</span><br><span class="line">191</span><br><span class="line">192</span><br><span class="line">193</span><br><span class="line">194</span><br></pre></td><td class="code"><pre><span class="line">\documentclass[11pt,twoside]&#123;ctexart&#125;</span><br><span class="line">\usepackage&#123;CJKnumb&#125;</span><br><span class="line">\usepackage&#123;amsmath,amssymb&#125;</span><br><span class="line">\usepackage&#123;calc&#125;</span><br><span class="line">\usepackage&#123;intcalc&#125;</span><br><span class="line">\usepackage&#123;ifthen&#125;</span><br><span class="line">\usepackage&#123;zref-user&#125;</span><br><span class="line">\usepackage&#123;zref-lastpage&#125;</span><br><span 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class="line">&#123;\begin&#123;minipage&#125;&#123;1.1\textheight&#125;</span><br><span class="line">\begin&#123;center&#125;</span><br><span class="line">\tiny \hdashrule[-3ex]&#123;\textheight&#125;&#123;\wol&#125;&#123;3pt&#125;\\[\smallskipamount]</span><br><span class="line">\makebox[0.6\textheight][s]&#123;装订线内不要答题&#125;\\[-3\smallskipamount]</span><br><span class="line">\hdashrule[-3ex]&#123;\textheight&#125;&#123;\wol&#125;&#123;3pt&#125;</span><br><span class="line">\end&#123;center&#125;</span><br><span class="line">\end&#123;minipage&#125; &#125;</span><br><span class="line">\fi</span><br><span class="line">&#125;</span><br><span class="line">%装订线结束</span><br><span class="line">%页眉设置结束</span><br><span class="line"></span><br><span class="line">%页脚设置开始</span><br><span class="line">\renewcommand&#123;\footrulewidth&#125;&#123;\wol&#125;</span><br><span class="line">\fancyfoot[C]&#123;\large&#123;&#123;\xingkai 微信公众号之数学的情怀&#125;\qquad 共\zpageref&#123;LastPage&#125;页\quad 第\thepage 页&#125;&#125;</span><br><span class="line">\newcounter&#123;ns&#125;</span><br><span class="line">\newcounter&#123;ts&#125;</span><br><span class="line">\newcounter&#123;nq&#125;</span><br><span class="line">\newcommand&#123;\wns&#125;&#123;\stepcounter&#123;ns&#125;\CJKnumber&#123;\thens&#125;、&#125;</span><br><span class="line">\newcommand&#123;\wq&#125;&#123;\stepcounter&#123;nq&#125;\thenq.&#125;</span><br><span class="line"></span><br><span class="line">%大题前计分表格</span><br><span class="line">\newcommand&#123;\tbs&#125;&#123;\begin&#123;tabular&#125;&#123;|c|c|c|&#125;\hline \makebox[\wot]&#123;得分&#125;&amp;\makebox[\wot]&#123;评卷人&#125;&amp;\makebox[\wot]&#123;复核人&#125;\\ \hline</span><br><span class="line"> &amp; &amp;\\ \hline\end&#123;tabular&#125;&#125;</span><br><span class="line"></span><br><span class="line">%排版大题前计分表格,序号,题型,大题说明</span><br><span class="line">\newcommand&#123;\ws&#125;[2]&#123;\raisebox&#123;-1ex&#125;&#123;\begin&#123;minipage&#125;[b]&#123;4.6\wot&#125;\tbs\end&#123;minipage&#125;&#125;</span><br><span class="line">\begin&#123;minipage&#125;[t]&#123;\textwidth-6\wot&#125; &#123;\heiti \wns #1 &#125; #2 \end&#123;minipage&#125; &#125;</span><br><span class="line">\makeatletter</span><br><span class="line">\zref@newprop&#123;totalsections&#125;[3]&#123;\arabic&#123;ns&#125;&#125;</span><br><span class="line">\zref@addprop&#123;LastPage&#125;&#123;totalsections&#125;</span><br><span class="line">\AtBeginDocument&#123;</span><br><span class="line">\setcounter&#123;ts&#125;&#123;\zref@extractdefault&#123;LastPage&#125;&#123;totalsections&#125;&#123;3&#125;&#125; &#125;</span><br><span class="line">\makeatother</span><br><span class="line">\linespread&#123;1.618&#125;</span><br><span class="line">\newcommand&#123;\D&#125;&#123;\,\mathrm&#123;d&#125;&#125;</span><br><span class="line">\newcommand&#123;\E&#125;&#123;\mathrm&#123;e&#125;&#125;</span><br><span class="line">\newcommand&#123;\dlim&#125;&#123;\displaystyle \lim &#125;</span><br><span class="line">\newcommand&#123;\dint&#125;&#123;\displaystyle \int &#125;</span><br><span class="line">\newcommand&#123;\sets&#125;[1]&#123;\&#123; #1 \&#125;&#125;</span><br><span class="line"></span><br><span class="line">\setCJKfamilyfont&#123;huawenxingkai&#125;&#123;华文行楷&#125; \newcommand*&#123;\xingkai&#125;&#123;\CJKfamily&#123;huawenxingkai&#125;&#125;%华文行楷</span><br><span class="line">\newcommand&#123;\dis&#125;&#123;\displaystyle&#125;</span><br><span class="line">\newcommand&#123;\Rank&#125;&#123;\mathrm&#123;Rank&#125;\mspace&#123;1mu&#125;&#125;</span><br><span class="line">\newcommand&#123;\Sign&#125;&#123;\mathrm&#123;Sign&#125;\mspace&#123;1mu&#125;&#125;</span><br><span class="line">\newcommand&#123;\rd&#125;&#123;\mspace&#123;1mu&#125;\mathrm&#123;d&#125;&#125;</span><br><span class="line">\newcommand&#123;\diag&#125;&#123;\mathrm&#123;diag&#125;\mspace&#123;1mu&#125;&#125;</span><br><span class="line">\newcommand&#123;\tr&#125;&#123;\mathrm&#123;tr&#125;\mspace&#123;1mu&#125;&#125;</span><br><span class="line">\newcommand&#123;\var&#125;&#123;\mathrm&#123;var&#125;&#125;</span><br><span class="line">\renewcommand&#123;\Re&#125;&#123;\operatorname&#123;Re&#125;&#125;</span><br><span class="line">\renewcommand&#123;\Im&#125;&#123;\operatorname&#123;Im&#125;&#125;</span><br><span class="line">\def\sgn&#123;\mathop&#123;\rm sgn&#125;&#125;</span><br><span class="line"></span><br><span class="line">%试卷头开始</span><br><span class="line">\begin&#123;document&#125;</span><br><span class="line">%试卷标题开始</span><br><span class="line">\begin&#123;center&#125;\vspace&#123;3mm&#125;</span><br><span class="line">      &#123;\xingkai \Large 第十届全国大学生数学竞赛试题&#125;\\[0.8mm]</span><br><span class="line">      &#123; $\left(\text&#123;非数学类, 2018年10月27日&#125;\right)$&#125;\\</span><br><span class="line">\end&#123;center&#125;</span><br><span class="line"></span><br><span class="line">%试卷标题结束</span><br><span class="line"></span><br><span class="line">%输出&quot;绝密&quot;字样</span><br><span class="line">&#123;\vspace&#123;-1.3mm&#125;\heiti 绝密$\bigstar$启用前&#125;\\[-4\bigskipamount]\\[-12mm]</span><br><span class="line">\begin&#123;center&#125;</span><br><span class="line">\vspace*&#123;2mm&#125;</span><br><span class="line">(16数学$-$胡八一)\\[3mm]</span><br><span class="line"> &#123;考试形式：\underline&#123;~闭卷~&#125;~\hspace&#123;2mm&#125;考试时间：\underline&#123;~~150~~&#125;分钟~\hspace&#123;2mm&#125;满分：~\underline&#123;~~100~~&#125;~分&#125;\\</span><br><span class="line"></span><br><span class="line">%根据大题数目自动生成计分总表</span><br><span class="line">\newcounter&#123;tc&#125;</span><br><span class="line">\newcounter&#123;tcsr&#125;</span><br><span class="line">\setcounter&#123;tc&#125;&#123;\value&#123;ts&#125;+3&#125;</span><br><span class="line">\setcounter&#123;tcsr&#125;&#123;\value&#123;tc&#125;-1&#125;</span><br><span class="line">\arrayrulewidth=2\wol </span><br><span class="line"></span><br><span class="line">\vspace*&#123;3.5mm&#125;</span><br><span class="line">\begin&#123;tabular&#125;&#123;|m&#123;3em&#125;&lt;&#123;\centering&#125;|*&#123;11&#125;&#123;m&#123;3.5em&#125;&lt;&#123;\centering&#125;|&#125;&#125;\hline</span><br><span class="line">         题~号 &amp; 一 &amp; 二 &amp; 三  &amp; 四 &amp; 五 &amp;六 &amp;七  &amp;总~~分 \\\hline</span><br><span class="line">		 满~分 &amp; 24 &amp; 8 &amp; 14  &amp; 12 &amp; 14  &amp;14 &amp;14 &amp;100    \\\hline</span><br><span class="line">	 	 得~分 &amp;    &amp;   &amp;     &amp;    &amp;     &amp;   &amp;  &amp;\rule&#123;0pt&#125;&#123;8mm&#125; \\\hline</span><br><span class="line">	\end&#123;tabular&#125;</span><br><span class="line">	\\\vspace*&#123;-1.5mm&#125;</span><br><span class="line">	\begin&#123;equation*&#125;</span><br><span class="line">	\begin&#123;aligned&#125;</span><br><span class="line">	\mbox&#123;注意：&#125;</span><br><span class="line">	&amp;1.\,\mbox&#123;所有答题都须写在试卷密封线右边,写在其他纸上一律无效&#125;.\hspace&#123;12.0cm&#125;\\</span><br><span class="line">	&amp;2.\,\mbox&#123;密封线左边请勿答题,密封线外不得有姓名及相关标记&#125;.\\</span><br><span class="line">	&amp;3.\,\mbox&#123;如答题空白不够,可写在当页背面,并标明题号&#125;.\\[-2mm]</span><br><span class="line">	\end&#123;aligned&#125;</span><br><span class="line">	\end&#123;equation*&#125;	</span><br><span class="line">\end&#123;center&#125;</span><br><span class="line"></span><br><span class="line">%试卷头结束</span><br><span class="line"></span><br><span class="line">\addvspace&#123;1\bigskipamount&#125;</span><br><span class="line"></span><br><span class="line">\ws&#123;\xingkai 填空题&#125;&#123;(\xingkai 本题满分24分，每题6分)\\&#125;\\\\</span><br><span class="line">\wq 设 $\alpha\in\left(0,1\right),\textrm&#123;则&#125;\displaystyle \lim_&#123;n\rightarrow +\infty&#125;\left(\left(n+1\right)^&#123;\alpha&#125;-n^&#123;\alpha&#125;\right)=$\underline&#123;0&#125;.\\</span><br><span class="line"></span><br><span class="line">\wq $\textrm&#123;若曲线&#125;y=f\left(x\right)\textrm&#123;是由&#125;\left\&#123;\begin&#123;array&#125;&#123;l&#125;</span><br><span class="line">x=t+\cos t\\</span><br><span class="line">e^y+ty+\sin t=1\\</span><br><span class="line">\end&#123;array&#125;\right.\textrm&#123;确定，则此曲线在&#125;t=0$ 对应点处的\\</span><br><span class="line">切线方程为\underline&#123;$y=1-x$&#125;.\\</span><br><span class="line"></span><br><span class="line">\wq $\displaystyle \int&#123;\displaystyle\frac&#123;\ln\left(1+\sqrt&#123;1+x^2&#125;\right)&#125;&#123;\left(1+x^2\right)^&#123;\frac&#123;3&#125;&#123;2&#125;&#125;&#125;&#125;dx=$\underline&#123;$\displaystyle \frac&#123;x&#125;&#123;\sqrt&#123;1+x^2&#125;&#125;\ln\left(x+\sqrt&#123;1+x^2&#125;\right)-\displaystyle \frac&#123;1&#125;&#123;2&#125;\ln\left(1+x^2\right)+C</span><br><span class="line">	$&#125;.\\</span><br><span class="line"></span><br><span class="line">\wq $\displaystyle\lim_&#123;x\rightarrow 0&#125;\displaystyle\frac&#123;1-\cos x\sqrt&#123;\cos 2x&#125;\sqrt[3]&#123;\cos 3x&#125;&#125;&#123;x^2&#125;=$\underline&#123;3&#125;.\\</span><br><span class="line">\newpage</span><br><span class="line">\ws &#123;\xingkai 解答题&#125;&#123;(\xingkai 本题满分8分)\\&#125;\\\\</span><br><span class="line">设函数$f(t)$在$t\ne 0$时一阶连续可导，且$f(1)=0$，求函数$f(x^2-y^2)$，使得曲线积分$\displaystyle \int_L&#123;y\left(2-f\left(x^2-y^2\right)\right)&#125;dx+xf\left(x^2-y^2\right)dy$</span><br><span class="line">与路径无关，其中$L$为任一不与直线$y=\pm x$相交的分段光滑闭曲线.</span><br><span class="line">\newpage</span><br><span class="line"></span><br><span class="line">\ws &#123;\xingkai 解答题&#125;&#123;(\xingkai 本题满分14分)\\&#125;\\\\</span><br><span class="line">设$f(x)$在区间$[0,1]$上连续，且$1\leqslant f\left(x\right)\leqslant 3$.证明：</span><br><span class="line">$$0\leqslant\int_0^1&#123;f\left(x\right)dx\int_0^1&#123;\frac&#123;1&#125;&#123;f\left(x\right)&#125;dx\leqslant\frac&#123;4&#125;&#123;3&#125;&#125;&#125;$$</span><br><span class="line">\newpage</span><br><span class="line"></span><br><span class="line">\ws &#123;\xingkai 解答题&#125;&#123;(\xingkai 本题满分12分)\\&#125;\\\\</span><br><span class="line">计算三重积分$\displaystyle\iiint\limits_&#123;\left(V\right)&#125;&#123;\left(x^2+y^2\right)&#125;dV$，其中$(V)$是由$x^2+y^2+\left(z-2\right)^2\geqslant 4$，$x^2+y^2+\left(z-1\right)^2\leqslant9$及$z\geqslant 0$所围成的空间图形.</span><br><span class="line">\newpage</span><br><span class="line"></span><br><span class="line">\ws &#123;\xingkai 解答题&#125;&#123;(\xingkai 本题满分14分)\\&#125;\\\\</span><br><span class="line">设$f(x,y)$在区域D内可微，且$\sqrt&#123;\left(\displaystyle\frac&#123;\partial f&#125;&#123;\partial x&#125;\right)^2+\left(\displaystyle\frac&#123;\partial f&#125;&#123;\partial y&#125;\right)^2&#125;\leqslant M$，$A\left(x_1,y_1\right),B\left(x_2,y_2\right)$是D内两点，线段AB包含在D内，证明：$f(x_1,y_1)-f(x_2,y_2)|\leqslant M|AB|$</span><br><span class="line"></span><br><span class="line">其中$|AB|$表示线段$AB$的长度.</span><br><span class="line">\newpage</span><br><span class="line"></span><br><span class="line">\ws &#123;\xingkai 解答题&#125;&#123;(\xingkai 本题满分14分)\\&#125;\\\\</span><br><span class="line">证明：对于连续函数$f(x)&gt;0$，有$\ln\int_0^1&#123;f\left(x\right)dx\geqslant\int_0^1&#123;\ln f\left(x\right)dx&#125;&#125;$</span><br><span class="line">\newpage</span><br><span class="line"></span><br><span class="line">\ws &#123;\xingkai 解答题&#125;&#123;(\xingkai 本题满分14分)\\&#125;\\\\</span><br><span class="line">已知$&#123;a_k&#125;$，$&#123;b_k&#125;$是正数数列，且$b_&#123;k+1&#125;-b_k\geqslant\delta &gt;0,k=1,2,\cdots $，$\delta$为一切常数，证明：若级数$\displaystyle\sum_&#123;k=1&#125;^&#123;+\infty&#125;&#123;a_k&#125;$收敛，则级数$\displaystyle\sum_&#123;k=1&#125;^&#123;+\infty&#125;&#123;\displaystyle\frac&#123;k\sqrt[k]&#123;\left(a_1a_2\cdots a_k\right)\left(b_1b_2\cdots b_k\right)&#125;&#125;&#123;b_&#123;k+1&#125;b_k&#125;&#125;$收敛.</span><br><span class="line"></span><br><span class="line">\mbox&#123;&#125;</span><br><span class="line">%试卷正文结束</span><br><span class="line">\end&#123;document&#125;</span><br></pre></td></tr></table></figure>
      
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